Federal Reserve Chairman Jerome Powell declined to voice clear support for the leaders of the Dallas and Boston Fed banks when asked about their recently disclosed stock trading and pledged to change the rules that allowed such market activity by policy makers.

Mr. Powell was responding to questions about stock trading by Dallas Fed leader Robert Kaplan and Boston Fed chief Eric Rosengren that was disclosed by their banks. The officials last year actively traded stocks and other investments, some of which are sensitive to...

Federal Reserve Chairman Jerome Powell declined to voice clear support for the leaders of the Dallas and Boston Fed banks when asked about their recently disclosed stock trading and pledged to change the rules that allowed such market activity by policy makers.

Mr. Powell was responding to questions about stock trading by Dallas Fed leader Robert Kaplan and Boston Fed chief Eric Rosengren that was disclosed by their banks. The officials last year actively traded stocks and other investments, some of which are sensitive to changes in monetary policy, while helping to set central bank policy.

Mr. Kaplan’s trading totaled many millions of dollars. Mr. Rosengren’s was more modest but included housing-related investments that can be affected by central bank actions.

In a press conference after the Fed’s policy meeting, Mr. Powell was asked if he had confidence in the two regional Fed leaders to stay in their jobs.

“In terms of having confidence and that sort of thing, I think no one is happy,” Mr. Powell said. “No one on the [Federal Open Market Committee] is happy to be—to be in this situation, to be having these questions raised. It’s something we take very, very seriously.”

The Fed has said it is reviewing its ethics rules and Mr. Powell on Wednesday said, “This is an important moment for the Fed and I’m determined that we will rise to the moment and can handle it in ways that will stand up over time.” He added, “I’m very reluctant to get ahead of the process and speculate…When we have things to announce we’ll go ahead and do that.”

All 12 regional Fed bank leaders were approved earlier this year for new five-year terms. Fed governor Lael Brainard, who ran the process, said at the time it was rigorous. But Mr. Powell on Wednesday said the financial disclosure forms weren’t on his radar and explained that the forms didn’t play a role in deciding then whether the officials would stay in their positions, as they all did.

“I was not aware of the specifics of what they were doing,” Mr. Powell said. Taking a look at the financial disclosure statements “has not been part of the process,” which instead has focused on broader leadership questions. “I wouldn’t blame the people who conduct that review” for being unaware of the trading, he said.

Last week, the Fed said it would undertake a formal review of the ethics rules that appeared to green light the regional presidents’ trading. While those codes advise senior leaders to avoid activities that would suggest any conflict of interest, they largely prohibited officials from buying bank stocks and limited trading around Federal Open Market Committee dates.

“We understand very well that the trust of the American people is essential for us to effectively carry out our mission, and that’s why I directed the Fed to begin a comprehensive review of the ethics rules around permissible financial holdings and activity by Fed officials,” Mr. Powell said Wednesday.

Messrs. Kaplan and Rosengren have defended their actions as consistent with their respective bank’s code of conduct policies, but said they would sell off individual stocks they own to avoid any appearance of a conflict of interest. They have turned down multiple requests for interviews to discuss their trading activity.

While the Fed board in Washington is part of the government, the 12 regional banks exist somewhere between public and private spaces. While overseen by the Fed, they are owned by member banks, have boards composed of private citizens, and their leaders are paid substantially more than Fed governors.

The regional Fed banks collect economic intelligence and their leaders participate in setting monetary policy. Additionally, the New York Fed implements monetary policy, and other regional Fed banks, like Boston, have played key roles in operating emergency-lending efforts. The leaders of the banks are privy to inside information on monetary policy as a result of their work.

Write to Michael S. Derby at michael.derby@wsj.com